Proportionality (mathematics)

About: Proportionality (mathematics) is a research topic. Over the lifetime, 375 publications have been published within this topic receiving 2990 citations. The topic is also known as: linearity & proportional to.

Diversity by proportionality: an election-based approach to search result diversification

Abstract: This paper presents a different perspective on diversity in search results: diversity by proportionality. We consider a result list most diverse, with respect to some set of topics related to the query, when the number of documents it provides on each topic is proportional to the topic's popularity. Consequently, we propose a framework for optimizing proportionality for search result diversification, which is motivated by the problem of assigning seats to members of competing political parties. Our technique iteratively determines, for each position in the result ranked list, the topic that best maintains the overall proportionality. It then selects the best document on this topic for this position. We demonstrate empirically that our method significantly outperforms the top performing approach in the literature not only on our proposed metric for proportionality, but also on several standard diversity measures. This result indicates that promoting proportionality naturally leads to minimal redundancy, which is a goal of the current diversity approaches.

The Efficiency of Fair Division

Abstract: In this paper we study the impact of fairness on the efficiency of allocations. We consider three different notions of fairness, namely proportionality, envy-freeness, and equitability for allocations of divisible and indivisible goods and chores. We present a series of results on the price of fairness under the three different notions that quantify the efficiency loss in fair allocations compared to optimal ones. Most of our bounds are either exact or tight within constant factors. Our study is of an optimistic nature and aims to identify the potential of fairness in allocations.

propr: An R-package for Identifying Proportionally Abundant Features Using Compositional Data Analysis.

Abstract: In the life sciences, many assays measure only the relative abundances of components in each sample. Such data, called compositional data, require special treatment to avoid misleading conclusions. Awareness of the need for caution in analyzing compositional data is growing, including the understanding that correlation is not appropriate for relative data. Recently, researchers have proposed proportionality as a valid alternative to correlation for calculating pairwise association in relative data. Although the question of how to best measure proportionality remains open, we present here a computationally efficient R package that implements three measures of proportionality. In an effort to advance the understanding and application of proportionality analysis, we review the mathematics behind proportionality, demonstrate its application to genomic data, and discuss some ongoing challenges in the analysis of relative abundance data.

KnightShift: Scaling the Energy Proportionality Wall through Server-Level Heterogeneity

Abstract: Server energy proportionality has been improving over the past several years. Many components in a system, such as CPU, memory and disk, have been achieving good energy proportionality behavior. Using a wide range of server power data from the published SPEC power data we show that the overall system energy proportionality has reached 80%. We present two novel metrics, linear deviation and proportionality gap, that provide insights into accurately quantifying energy proportionality. Using these metrics we show that energy proportionality improvements are not uniform across various server utilization levels. In particular, the energy proportionality of even a highly proportional server suffers significantly at non-zero but low utilizations. We propose to tackle the lack of energy proportionality at low utilization using server-level heterogeneity. We present Knight Shift, a server-level heterogenous server architecture that introduces an active low power mode, through the addition of a tightly-coupled compute node called the Knight, enabling two energy-efficient operating regions. We evaluated Knight Shift against a variety of real-world data center workloads using a combination of prototyping and simulation, showing up to 75% energy savings with tail latency bounded by the latency of the Knight and up to 14% improvement to Performance per TCO dollar spent.